Swaps

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## Swaps

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**Nature of Swaps**A swap is an agreement to exchange cash flows at specified future times according to certain specified rules**An Example of a “Plain Vanilla” Interest Rate Swap**• An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million • Next slide illustrates cash flows**---------Millions of Dollars---------**LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2% Sept. 1, 1998 4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10 Sept. 1, 1999 5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25 Sept. 1, 2000 5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45 Cash Flows to Microsoft(See Table 6.1, page 127)**Converting a liability from**fixed rate to floating rate floating rate to fixed rate Converting an investment from fixed rate to floating rate floating rate to fixed rate Typical Uses of anInterest Rate Swap**Intel and Microsoft (MS) Transform a Liability(Figure 6.2,**page 128) 5% 5.2% Intel MS LIBOR+0.1% LIBOR**Financial Institution is Involved(Figure 6.4, page 129)**4.985% 5.015% 5.2% F.I. MS Intel LIBOR+0.1% LIBOR LIBOR Dealer spread = .03% evenly split**Intel and Microsoft (MS) Transform an Asset(Figure 6.3, page**128) 5% 4.7% Intel MS LIBOR-0.25% LIBOR**Financial Institution is Involved(See Figure 6.5, page 129)**4.985% 5.015% 4.7% F.I. MS Intel LIBOR-0.25% LIBOR LIBOR Dealer spread = .03 %**Fixed**Floating AAACorp 10.00% 6-month LIBOR + 0.30% BBBCorp 11.20% 6-month LIBOR + 1.00% The Comparative Advantage Argument (Table 6.4, page 132) • AAACorp wants to borrow floating • BBBCorp wants to borrow fixed**The Comparative Advantage Argument**• AAACorp has absolute advantage in both markets • But a comparative advantage in fixed • BBBCorp has comparative advantage in floating • If AAA borrows fixed, the gain is 1.2% • If BBB borrows floating, the gain is reduced by .7% • Therefore, we have a net gain of 1.2 - .7 = .5% • If the gain is split evenly, we have a gain per party of: G = (1.2 - .7)/2 = .25%**Swap Design**• Design the swap so AAA’s borrowing rate equals the comparative disadvantage (CD) rate minus the gain: • LIBOR + .3 - .25 • Do the same thing for BBB • BBB’s rate with swap: • 11.2 - .25 • Now, draw the diagram**The Swap (Figure 6.6, page 132)**9.95% 10% AAA BBB LIBOR+1% LIBOR The floating rate leg should be LIBOR**Swap Design with FI**• Adjust swap gain for dealer spread • Suppose dealer spread = .04% • Then gain: • G = (1.2 - .7 - .04)/2 = .23% • AAA’s rate with swap: • LIBOR + .3 - .23 = LIBOR + .07 • BBB’s rate with swap: • 11.2 - .23 = 10.97% • Draw swap diagram**The Swap when a Financial Institution is Involved (Figure**6.7, page 133) 9.93% 9.97% 10% AAA F.I. BBB LIBOR+1% LIBOR LIBOR Check that dealer spread = .04%**Criticism of the Comparative Advantage Argument**• The 10.0% and 11.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates • The LIBOR+0.3% and LIBOR+1% rates available in the floating rate market are six-month rates • BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future**Valuation of an Interest Rate Swap**• Interest rate swaps can be valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond**Swap Valuation**• Fixed Receive: Vswap = Vfixed – Vfloating • Fixed Pay: Vswap = Vfloating - Vfixed • The fixed rate stream is valued as an annuity • The floating rate stream is valued by noting that it is worth par immediately after the next payment date**Floating Rate Perpetuity**• To create a floating rate perpetuity, invest principal value in 6-month LIBOR • At the end of 6-months, remove the interest and reinvest the principal value at the new 6-month LIBOR • Therefore, the cost of a floating rate perpetuity is principal value • It always sells for its par value immediately after interest payment**Floating Rate Instrument with Maturity T**• At the end of T years, floating rate perpetuity is worth the principal value M • Therefore, the floating rate instrument is worth: M – MdT • Or M - M/(1+y/2)2T, where is the rate on a zero-coupon bond maturing in T years**Swap Valuation**• The floating rate instrument is worth: Vfloating = M – M/(1+y/2)2T • The fixed rate stream is worth: Vfixed = (C/2)(Annuity Factor) • So for Fixed Receive Swap: Vswap = (C/2)(Annuity Factor) - M +M/(1+y/2)2T**Swap Valuation**• The swap is structured such that initial value is zero to either party • Set Vswap = 0 • Rearrange terms: M=(C/2)(Annuity Factor) + M/(1+y/2)2T • The left-hand side is the present value of a bond at y • Since the bond is selling at par, CR = C/M = y • For the swap to have zero value the fixed rate must equal the yield to maturity on a par bond • The swap rate is the coupon rate on a LIBOR bond that causes it to be worth par**Example**• Zero coupon LIBOR curve is 5%, 6%, and 7% for one, two, and three years • What is the swap rate on a three year interest rate swap? • Assume payments are annual and yields are compounded annually • Solve for LIBOR par yield • M = CRxM(d1 + d2 + d3) + Md3**Example Continued**• Solution:**Interest Rate Risk**• Receive Fixed: Vswap = Vfixed – Vfloating • Pay Fixed: Vswap = Vfloating – Vfixed**An Example of a Currency Swap**An agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US$ principal of $15,000,000 every year for 5 years**Exchange of Principal**• In an interest rate swap the principal is not exchanged • In a currency swap the principal is exchanged at the beginning and the end of the swap**Three Cash Flow Components**• t = 0: exchange principal based upon current exchange rates Pay: $15 M Rcv: £ 10 M • t = 1, 2, 3, 4, 5: Pay: .11x10 = £1.1 M Rcv: .08x15 = $1.2 M • t = 5: Pay: £ 10 M Rcv: $ 15 M**The Cash Flows (Table 6.6, page 140)**Dollars Pounds $ £ Years ------millions------ 0 –15.00 +10.00 +1.20 1 –1.10 2 +1.20 –1.10 3 +1.20 –1.10 4 +1.20 –1.10 5 +16.20 -11.10**Conversion from a liability in one currency to a liability**in another currency Conversion from an investment in one currency to an investment in another currency Typical Uses of a Currency Swap**USD**AUD General Motors 5.0% 12.6% Qantas 7.0% 13.0% Comparative Advantage Arguments for Currency Swaps (Table 6.7, page 141) General Motors wants to borrow AUD Qantas wants to borrow USD**Comparative Advantage**• GM has absolute advantage in both markets • But GM has comparative advantage in dollars • Qantas has comparative advantage in Australian dollars • So GM should borrow dollars and Qantas Australian dollars • Then swap cash flows to earn gain from comparative advantage**Comparative Advantage**• Gain per party: G = (2 - .4)/2 = .8% • GM’s rate with swap: 12. 6 - .8 = AUD 11.8% • Qantas’ rate with swap: 7 - .8 = USD 6.2%**Qantas Assumes Exchange Rate Risk**USD 5% USD 5% AUD 13% GM Qantas AUD 11.8%**GM Assumes Exchange Rate Risk**USD 6.2% USD 5% AUD 13% GM Qantas AUD 13.0%**FI Assumes Exchange Rate Risk**• Adjust swap gain for dealer spread • Suppose dealer spread = .2% • Then gain: • Gain per party: G = (2 - .4 - .2)/2 = .7% • GM’s rate with swap: 12. 6 - .7 = AUD 11.9% • Qantas’ rate with swap: 7 - .7 = USD 6.3%**FI Assumes Exchange Rate Risk**USD 5% USD 6.3% USD 5% GM F.I. Q AUD 13% AUD11.9% AUD 13% Check that dealer spread = .2% Pay: 13.0 – 11.9 = AUD 1.1% Rcv: 6.3 – 5.0 = USD 1.3%**Valuationof Currency Swaps**Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts**Swaps & Forwards**• A swap can be regarded as a convenient way of packaging forward contracts • The “plain vanilla” interest rate swap in our example consisted of 6 Fraps • The “fixed for fixed” currency swap in our example consisted of a cash transaction & 5 forward contracts**Swaps & Forwards(continued)**• The value of the swap is the sum of the values of the forward contracts underlying the swap • Swaps are normally “at the money” initially • This means that it costs nothing to enter into a swap • It does not mean that each forward contract underlying a swap is “at the money” initially**Credit Risk**• A swap is worth zero to a company initially • At a future time its value is liable to be either positive or negative • The company has credit risk exposure only when its value is positive